Cremona's table of elliptic curves

34485 = 3 · 5 · 11² · 19

Field	Data	Notes
Atkin-Lehner	3- 5- 11- 19-	Signs for the Atkin-Lehner involutions
Class	34485s	Isogeny class
Conductor	34485	Conductor
∏ cp	200	Product of Tamagawa factors cp
deg	720000	Modular degree for the optimal curve
Δ	-878635434638671875 = -1 · 35 · 510 · 117 · 19	Discriminant
Eigenvalues	2 3- 5-  2 11-  1 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,214130,24140749]	[a1,a2,a3,a4,a6]
Generators	[298:45371:8]	Generators of the group modulo torsion
j	612911999504384/495966796875	j-invariant
L	15.674163673501	L(r)(E,1)/r!
Ω	0.1810811261067	Real period
R	0.43279396396798	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	103455u1 3135h1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 34485s1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
2	-	-	2	-	1	-3	-	-6	0	2	8	-12	-4	-12	-1	-5	-12	-12	-3	-14	-5	-9	15	8

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Quadratic twists for elliptic curve 34485s1

-3	-11
103455u1	3135h1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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